On spatial decay estimates for derivatives of vorticities with application to large time behavior of the two-dimensional Navier-Stokes flow

In this paper we establish spatial decay estimates for derivatives of vorticities solving the two-dimensional vorticity equations equivalent to the Navier-Stokes equations. As an application we derive asymptotic behaviors of derivatives of vorticities at time infinity. It is well known by now that the vorticity behaves asymptotically as the Oseen vortex provided that the initial vorticity is integrable. We show that each derivative of the vorticity also behaves asymptotically as that of the Oseen vortex.